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WASHINGTON — As much as one-third of President Obama’s goal of reducing defense spending by $400 billion may be achieved by cutting overhead, putting more risk on contractors and eliminating overlapping and marginal programs, former Defense Secretary Robert Gates said.

“The sort of back-of-the-envelope numbers we’ve run would suggest we could get at least a third of the money we need,” or more than $120 billion, Gates said in an interview with Bloomberg News.

“We can probably get out more efficiencies and marginal programs — or where we have redundancy in the services,” he said. “For 2012 and 2013, my hope is the cuts won’t be too deep, but I think that there is more room with efficiencies.”

Still, he said he wasn’t “sanguine” that the long-term savings can be achieved.

“This is going to be hard,” said Gates, whose replacement, Leon Panetta, was sworn in yesterday. “Tough choices are going to have to be made, and I want the Congress and president to understand what those tough choices are.”